Finite Group DatabasebetaFinite Group Databasebeta| order | 6116 |
| automorphism | Aut(G) order 4220040 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3058 |
| direct product | C2×D1529 |
| unambiguous semidirect product | (C2×C11)⋊D139 |
| unambiguous semidirect product | (C2×C139)⋊D11 |
| Fitting, socle | C2×C11×C139 ⋊ C2 |
| derived, Hall | C11×C139 ⋊ C22 |
| Sylow | C139 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D139 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1529 |
| commutator, hypocenter | C11×C139 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C139 | C2 |
| LCS | G ▷ C11×C139 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
1532 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11⋊(D139⋊C3), D3×D1529, C2×D4587, … |
| maximal normal subgroup of | C2×C11⋊(D139⋊C3), C2×C3×D1529, C2×(C11⋊C5)⋊D139, … |
| maximal quotient of | D3×D1529, C2×D4587, C2×C3×D1529, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6116, 7);